Slide-rule.



w. A. WARMAN.

sums RULE. AP-PLICATION FILED DEC. 22. I914.

Patented Sept. 24, 1918.

4 SHEETS-SHEET 1.

W. A. WAHMAN.

SL'IDE RULE.

APPLICATION FILED DEC. 22. 1914.

1 ,2795798 Patented Sept. 24, 1918,

4 SHEETS-SHEET 2.

[III II llll ll W. A. WARMAN.

SLIDE RULE.

W. A. WARMAN.

SLIDE RULE.

APPLICATION FILED DEC. 22. 19:4.

Patented Sept. 24, 1918;

4 SPlEETS-SHEET 4.

UNITED STATES PATENT OFFICE.

WILLIAM A. WAR/MAN, OF NEW YORK, N. Y;, ASSIGNOR 'IO KELLER MECHANICALENGRAVING COMPANY, OF NEW YORK, N. Y., A CORPORATION OF NEW YORK.

SLIDE-RULE.

Specification of Letters Patent.

Patented Sept. 24, 1918.

Application filed December 22, 1914. Serial N 0. 878,491.

- To all whom it may concern:

Be it known that I, WILLIAM A. WARMAN, a citizen of the United States,and a resident of New York, borough of Manhattan, in the county of NewYork and State of New York, have made and invented certain new anduseful Improvements in Slide-Rules, of which the following is aspecification.

My invention relates to calculating machines or implements of thecircular slide rule type in which operations involving multiplicationand division are performed by. adding or subtracting logarithms by meansofscales divided logarithmically and movable relative to one another;and com} rises a slide rule device having scales carried by membersmovable relatively to one another about a common axis, and which scalesare so divided and graduated that problems involving hours andfractional parts of an hour may be performed directly, and without firstreducing the fractional parts to their decimal equivalents as isnecessary in using a slide rule the scales of which aregraduateddecimally, the numerals associated with the points of division of ascale of my improved slide rule indicating numbers and fractional parts(not decimal) thereof, instead of numbers and decimal parts thereof asis commonly the case in slide rules.

A further object of my invention is to,

provide in combination with the logarithmic scales of the device,certain scales divided and graduated in equal parts for the purpose ofadding time intervals to thus determine the total time consumed upon aparticular.

operation, the time thus determined to be then used as a factor inmultiplication or division operations to be performed by the logarithmicscales of the device. a

A further object of my invention is to provide a circular slide rulehaving certain locking mechanism for holding the several members whichconstitute the same in proper definite relations with one another afterthey have been adjusted preparatory to uslng'the rule.

My improved calculating machine or circular slide rule is designedparticularly for use in computing pay rolls in manufacturingestablishments wherein the numerous workmen commonly work for varioustimes measured in hours and fractional parts thereof (commonly 12ths as5 minute intervals are the shortest taken account of), at rates basedupon various rates per week, the number of hours of which again vary indifferent establishments It also follows that the cost of the laborexpended upon a given manufactured able in the same way.

'VVith the above and other objects of invention in view, my inventionconsists in the circular slide rule device illustrated in theaccompanying drawings and hereinafter described and claimed, and in suchvariations and modifications thereof as will be obvious to those skilledin the art to which my inalso the way in which the scales aredivided andgraduated or marked;

product is determin- Fig. ,4. is a similar View illustrating a modifiedsystem of the scales;

Fig. 5 is a view drawn to a larger scale and showing certain looking orclamping graduation for two of mechanism forming apart of my device,this view being taken upon a longitudlnah plane indicated by the line5--5, Fig.7

Fig. 6 is a similar view but taken upon a plane indicated by the line6-6, Fig. 7; and

Fig. plane indicated by the line 77, Fig. 5.

In the drawings the reference characters 5, 6 designate two wheelsadjustable about 7 is a view taken upon a transverse an axle 7 and uponthe peripheries of which wheels the various scales used in performingmathematical problems by the rule are engraved or otherwise placedalthough 1t will be understood that my invention is equally applicableand includes slide rule devices in which the various scales are im'pressed upon circular disks, asdistinguished I ting the scales, andtogether in bringing the divisions of the scales into a position to beread conveniently.

The reference character 10 designates a runner supported from the axle 7by means of arms 11 and extending across the faces of the wheels asshown in Figs. 1 and 3, the

runner commonly having a transparent window through .which the scalesmay be seen, and a line engraved thereupon for use in setting the scalesand in reading results;

from them. The transparent portion of the runner has a vernier 12, Fig.3, engraved upon it'and divided logarithmically for use in readingnumerical quantities to four figures as will be hereinafter explained,and also a second Vernier 13 for use in reading one of the scales.

The runner may be moved about the axle relative to the wheels as will beunderstood, and the same carries two graduated scales 14, 15, the use ofwhich will be hereinafter explained.

The various scales upon the wheels 5, 6, and the manner in which theyare sub-divided, graduated, and arranged, is as follows:

v The scales A and B extend throughout the entire circumference of thewheels and are ordinary logarithmic scales each sub-divided into 100parts and graduated from 1 to 100, the distance from the beginning ofthe scales to the several points of division being proportionate to thelogarithms of the numbers placed at the points of division, as is alwaysthe case in scales divided logarithmically. These scales obviously readto three figures directly, and to four figures by the use of the vernier12 above referred to in connection with the diagonal lines connectingthe several successive points of division. They are obviously theequivalent of the C and D scales of an ordinary slide, rule, and may beused to solve problems involving multiplication, division and proportionin the same manner as with an ordinary slide rule, the result being readdirectly to three figures, or to four figures by using the Vernier.

Adjacent the scale A on the wheel 5 are three scales D, E and F eachextending throughout the entire circumference of the wheel and whichscales are referred to as hour scales for the reason that while'each issub-divided logarithmically in the same manner as the scales A and B(although E and F need not be so finely sub-divided as A), the numeralsplaced at the various points of division represent hours and fiveminute-intervals, the spaces thus representing units and twelfthsthereof, instead of units and tenths as in a logarithmic scale as it isordinarily graduated. Thus the scale F is sub-divided into twelve parts,each representing five minutes, and the entire scale representing onehour. The scale E is graduated from one to ten hours, each divisionrepresenting five minutes, while the scale D is graduated from ten toone hundred hours, the major sub-divisions being sub-divided each intotwelve parts and graduated to read intervals of five minutes each. Anyinterval from five minutes to one hundred hours varying by intervals offive minutes may therefore be read upon one or another of the threescales in question. From the foregoing it follows that any givenquantity of time in hours and minutes read from the figures upon thehour scales is reduced to hours and tenths of an hour, or to tenths ofan hour; and that it isnot necessary to reduce the five minuteintervalsor twelfths of an hour in which time is commonly measured todeciequivalents of an hour. This is best done by employing the method ofproportion as used in slide rule practice, as follows, assuming 54 hoursas constituting a weeks work, and a rate of $24.00 per week. In such acase, by setting 54 on the scale D opposite 24 on the scale B, the costsor wages corresponding with any given number of hours or five minuteintervals thereof read on either the scales D, E or F (which isobviously a known quantity), may be read directly from the scale B, theproportion being expressed as follows: 54: 24: time: X.

As thus set, and without changing the rel ative position of the wheels,we will find opposite five minutes on the scale F, 3700 on the scale B;and opposite 30 minutes on F, 2220 on B. Reading time on the scale E wewill find 1333 on the scale B opposite three hours; and reading time onthe scale D we will find 2244 on B opposite 50 hours and 30 minutes.These quantities are obviously read as significant figures and withoutreference to their actual values, as is always the case in using a sliderule. They represent, however, in dollars and cents, $.O37,$.222,$1.333. and $22.44, these being obviously the costs of or wages for 5minutes, 30 minutes, 3 hours. and 50 hours 30 minutes time or work at arate of $24.00 per week of 54 hours. The cross line on the runner willobviously be usedin setting the scales, and in reading from one scale toan-- other, as in an ordinar slide rule; and the product or result wilbe read decimally upon the scale B notwithstanding the fact that thetime on the hour scales is read. ther on in hours and twelfths.

A further use of the scales D, E and F is in multiplying or dividingtime read upon said scales by an abstract multiplier or divisor, theprocess being identical with like processes performed by the use of thedecimally graduated scales of an ordinary slide rule, the result,however, being read from the hour scales in hours and minutes, insteadof decimally as is the case in slide rule practice. Thus, formultiplication, the index point or 1 of B is set opposite any known time(multiplicand) indicated upon the scales D, E or F; then opposite themultiplier on the scale B the product is read'upon the hour scalesdirectly in hours and minutes.

- In performing examples in division, the divisor on the scale B is setopposite the dividend indicated in hours and minutes upon the scales D,E or F; and the quotient read in hours and minutes upon the hour scalesopposite 1 on the scale B; the dividend and quotient being read in hoursand minutes, as distinguished from in hours and decimal parts orhundredths thereof, as in ordinary operations with a slide rule.

' It will also be obvious that thescales B and the hour scales may beused in solving problems involving feet and inches (or twelfths) andWithout first reducing the inches to decimal equivalents of a foot, theresult or answer being read on the hour scales directly in feet andinches. 1

The scale T is a logarithmic scale of tangents, and the scale B Icorresponds with the scale B but is reversed or inverted with referencethereto. The use of these scales is the same as with an ordinary sliderule and further reference to them is unnecessary as they are notinvolved in the invention to which this application relates.

The scale C upon the wheel 6 is a logarlthmic scale graduated from 1 'to100 and extending throughout one-half the circumference of the wheel, sothat the combined length of two such scales corresponds with the lengthof the scale B. The scale C is similar to the double A scale of anordinary Mannheim rule, and is used in connection with the scale B infinding the square or the square root of numbers in the same manner aswith an ordinary slide rule. The arrangement of this scale adjacent thescale B, hoW- ever, permits problems involving the square or square rootof numbers to be more readily solved than with an ordinary slide rule inwhich the slide is located between the scales used in such operations,as the result may be read without using the runner, whereas in theordinary slide rule the runner must be used because the slide liesbetween the two paragraph are ordinary slide rule scales, and

are not involved in the invention disclosed in'this application.

Located at the left-hand edge of the wheel 5 is a scale G extendingthroughout the circumference of the wheel and divided into 100 maindivisions and graduated accordingly, each major division beingsub-divided into 12 parts to indicate 5 minute intervals, the majordivisions indicating hours. The right-hand edge of the wheel 6 isdivided and sub-divided in the same way to provide a scale H, but thepoints of division are graduated from 1 to 12, designating hours andlive minute intervals, and the graduations repeated, 8 and 3; such shortor 12 hour scales occurring in succession and collectively forming thescale H.

The scales G and H are used to add several time intervals to determinethe entire time worked by a workman during a day or week, or todetermine the total time devoted to a particular piece of work, in thesame way as ordinary addition scales. For instance, if three hours 15minutes is to be added to four hours 35 minutes, any numeral 12 upon thescale H (which corresponds with the zero points of the severalsuccessive scales which make up the scale H) is placed opposite 4: hours35 minutes upon the scale and, opposite 3 hours 15 minutes upon H, Weread the result, 7 hours 50 minutes upon G. The runnermay then be set tothis value on G, and an additional time interval added to the amountonGr by again setting 12 on the scale H to the runner, that is, to 7hours 50 minutes, and, opposite the time to be added read 011 H, the newsum may be read on G. Any number of time intervals may thus beaccumulated on G, and the result used as a factor in multiplying bymeans of the hour scales and the scale B, as above pointed out. Duringthis addition process it will be obvious that any one of the several 1to 12 scales which make up the scale H may be used to measure theincrement to be added to the amount already accumulated upon the scaleG.

Another use of the scales G and H is to determine the time intervalbetween two clock times. For example, to find the time interval between8:15 A. M. and 5 d5 P. M., we set any scale division indicating 8 hoursand 15 minutes upon the scale H opposite the zero point on the scale G,and read the result (9 hours minutes) on G, opposite the scale divisionindicating 5 hours 45 minutes On the next succeeding 1 to 12 section ofthe scale H. g

The scales 14, 15 carried by the runner 10 are for the purpose ofsubtracting from a given interval of time an intervening interval oflost time, as time taken for lunch; or for deducting time during which aworkman is not working upon a given piece of work. This may be done byfirst finding the total time as above, disregarding the time to bededucted, and then reading back along the scale it from the total timeindicated on G, the time to be deducted. The zero points of the scales14:, 15 correspond with the reading line on the runner, so that the actof reading from H to G automatically sets the zero point of the scale 14at the division on G indicating the total time interval from which thelost time is to be deducted.

The same end may be accomplished by in effect using the scales H and 15as additional scales, as will be understood by the following example:Required to find the total time worked during the day by a workmanbetween the hours of 7 and 11 A. M. and 12 and 5 P. M. e set 7 on thescale H opposite zero on the scale G, then set 2 on the scale 15opposite 11 on the scale H, and read the result (7 hours) on the scale Gopposite 5 on the scale 15, it being noted that the 2 selected on thescale 15 should be the one beyond the zero point of the scale, asotherwise the interval to be deducted would in fact be added to theinterval be- Y tween the two extreme clock times.

the same as the scales hereinbefore described,

and are not shown in detail. The left-hand edge of the wheel 5, however,is provided with a scale divided into 360 equal parts in place of thescale G, and the right-hand edge of the wheel 6 is likewise divided into360 parts arranged in 12 successive scales of 30 divisions each. Monthsare engraved between the several successive scales, so that theright-hand scale represents 12 months of 30 days each as is assumed inpractice in interest computations, while the left-hand scale representsa year of 360 days as used in figuring interest. If, then, any given dayof any month read on the right-hand scale be set opposite zero of theleft-hand scale, then opposite any successive date on the right-handscale the number of days between the two dates may be read from the uresthe reference characters 16, 17 designate the bulbs of the wheels 5, 6;and 18, 19, 20 designate three sliding members or bars located within a.passage extending longitudinally of the axle 7 These bars are providedwith inclined cam surfaces as shown at 21, 22, 23, which engage keys 24,25, 26 located in recesses in the axle 7 and force them outward againstthe inner surfaces of the hubs of the wheels andrunner arms 11 when thebars are moved longitudinally within the passage in the axle. A yoke 27is secured to one end of the axle 7 which yoke supports an oscillatingoperating member 30 having three projections 31, 32, 33 adapted toengage the ends of thebars 18, 19, 20 and move them toward the left, tothereby operate the keys 24, 25, 26, the particular key operateddepending upon which one of the bars is operated. It therefore followsthat by a proper manipulation of the operating member 30 by means of thehandle 34: the runner and either one of the wheels may be locked to theaxle by means of one of the keys, 24, 26; and that both wheels may belocked to the axle by means of the key 25. A spring 35 is provided forforcing the bars toward the right, the end of which bears against a disk36, which disk rests against the left-hand ends of the bars. I

It will of course be understood that the axle 7 is rotatable in thebearings providedfor it at the upper ends of the pedestals or supports9, so'that after the runner and either wheel are clamped or locked tothe axle, or after the two wheels are-clamped to the axle, the partsthus clamped or locked together, together with the axle, may be rotatedto bring the scales into a position such that they may be read withconvenience.

Having thus described and explained my rotatable axle having a passageextending longitudinally thereof; means for support ing said axle; twowheels supported by said axle and rotatable thereupon, and the pe-"ripheries of which wheels carry scales for performing mathematicalcalculatlons; a movable runner supported from said axle and extendingacross the peripheries of said wheels; and means located within thepassage aforesaid for locking said runner and either one of said wheelsto said axle, and for locking both said wheels to said axle.

:2. In a device of the class described, a rotatable axle having apassage extending longitudinally thereof; means for supporting saidaxle; two wheels supported by said axle and rotatable thereupon, theperipheries of which wheels carry scales for performing mathematicalcalculations; a movable runner supported from said axle and extendingacross the peripheries of said wheels; three reciprocating memberslocated within the passage aforesaidand having each an inclined camsurface; means for moving said reciprocating members; and three keyslocated in recesses formed in said axle and in engagement one with eachof said cam surfaces and which keys extend to the periphery of saidaxle. Y 3. In a device of. the class described, a rotatable axle havinga passageextending longitudinally thereof; means for supporting saidaxle; two wheels supported by said axle and rotatable thereupon, and theperipheries of which wheels carry scales for performing mathematicalcalculations; a movable runner supported from said axle and extendingacross the peripheries of said wheels; three reciprocating memberslocated within the passage aforesaid and having each an inclined camsurface; three keys located in recesses formed in said axle and inengagement one with each of said cam surfaces and which keys extend tothe periphery of said axle; and an oscillating operating member carriedby said axle and having projections adapted to engage and operate saidreciprocating members.

4:. A slide rule mechanism comprising a rotatably mounted axle, twowheels arranged side by side rotatably mounted thereon, hubs spaced tothe sides of said wheels and rotatably mounted upon said axle, a runnerex tending across the periphery of said wheels and secured to saidspaced hubs and carried thereby, means housed within said axle adaptedto lock together said wheels and said runner-carrying hubs.

5. A calculating instrument of the class described comprising two wheelsarranged adjacent to one another, the periphery of one of said wheelshaving a logarithmically divided scale graduated to read in integers anddecimal fractional parts thereof, and a, second scale divided into equalparts and graduated to read in hours and minutes; and the periphery ofthe adjacent wheel having a logarithmic scale graduated to read in hoursand minutes, and a second scale divided into equal parts and graduatedto read in hours and minutes.

6. A calculating.instrument of the class described comprising twomembers movable relative to each other, and each of which carries alogarithmically-divided scale, which scales are of equal length; thescale upon one of said members being graduated to read in units andtenths thereof, or decimally; and the scale upon the other of saidmembers being graduated so as to read in units and twelfths thereof.

Signed at New York, borough of Man hattan, in the county of New York andState of New York, this 17 day of December, A. D. 1914.

WILLIAM A. WARMAN.

Witnesses:

ANNA V. VVALSH, GEORGE E. (3001:.

